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The greatest common factor is found by finding the product of common primes.

91=713, 104=22213  so the gcf of 91 and 104 is 13.  Since the highest power of x and y in both terms is 1, the hcf for the variables is just xy

13xy

Answer:  The correct option is (A) 13xy.

Step-by-step explanation:  We are given to select the greatest common factor (G.C.F) of the following two expressions :

\(91x^2y~~~~\textup{and}~~~~104xy^3.\)

The G.C.F. of two numbers is the product of the common terms in the prime factorization of the expressions.

We have

\(91x^2y=7\times 13\times x\times x\times y,\\\\104xy^3=2\times2\times2\times13\times x\times y\times y\times y.\)

Therefore, the G.C.F. of the given expressions will be

\(G.C.F.=13\times x\times y=13xy.\)

Thus, the required G.C.F is 13xy.

Option (A) is CORRECT.

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